Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of AΣL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C32×AΣL(1,𝔽16) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C32 | #99 |
| commutator | C23 | C22×C32×C4 |
| Frattini, cosocle | C2×D4 | C23×C32 |
| prime radical | C2×C32×#120 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C23×C32 ◁ C22×C32×D4 ◁ G | |
1314 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2)(11,12,13);(3,4)(5,9,10,7)(6,8)(14,15,16);(4,7)(8,9)234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 3178);